Damped paddle wheel for plasma chamber shock tube

ABSTRACT

A damping gyrometer comprised of at least two and preferably four rotating paddles attached to a common central elevated low-friction pivot point via rising radial arms. A stand with a concave glass element provides a low-friction support as a pivot point seat for the pivot point. All elements of the apparatus are non-conductive. Once set into motion, the only force acting on the gyrometer are the pivot point friction and the damping effects of the medium in which it spins. A laser beam and photodetector (or alternatively a laser displacement sensor), along with customized software algorithms are used to measure the rotational rate and, hence, the deceleration rate of the apparatus which can then be used to determine properties of the medium in which it spins, including changes in density, pressure, and temperature. The measurement can also be directly related to the electron density in the case of weakly ionized gases.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of prior filed co-pending U.S.Provisional Patent Application No. 60/174,737,filed on Jan. 6, 2000.

FIELD OF THE INVENTION

The present invention relates generally to sensors for measuring theproperties of a gaseous medium and, more specifically, to a dampinggyrometer for measuring the properties, e.g., temperature, of a gaseousmedium based on the measured damping effects that are principally causedby thermally induced viscosity changes.

BACKGROUND OF THE INVENTION

Many recent experiments involving the study of the interaction of weaklyionized gases and moving bodies have yielded anomalous observations thatare not explained satisfactorily according to currently understoodphenomena. The fractional degree of ionization needed to see the effectsare on the order of 10⁻⁶. Most of these effects are easiest to observeunder highly energetic flow conditions. The most striking andpotentially the most valuable effect concerns measurable changes inshock profiles, shock velocities and shock intensities.

Modified shockwaves can alter the way that an air vehicle interacts withits environment. In a dynamic flow setting where a vehicle surface isinteracting with the weakly ionized gas, these effects can be translatedinto drag and surface heating rate variations that potentially afford animportant mechanism for solid-state electronic control. The long-rangegoal of the study of these interactions is to understand the processessufficiently to be able to apply them to optimizing the systems-levelperformance of aerodynamic vehicles.

Although the most striking measurable effects are seen under highlyenergetic flow conditions, these conditions are inherently difficult tostudy when trying to understand the basic physical processes thatunderlie the observed system behavior. The conditions are highlyunsteady and measurements require the use of high-speed data acquisitionsystems. In addition, the electronic mechanisms for producing the weaklyionized gas can introduce excessive noise into the measurement system.

On a systems level, there is a price to be paid for the observedaerodynamic effects in terms of the input power needed to alter themedium. Some portion of the observed effects can often be attributed tothe natural Joule-heating of the medium. It is necessary to separate theheating effects from “other” energy exchange mechanisms to understand ifthere is any novel aspect that is attributable to the ionization.Possible “other” mechanisms include non-equilibrium energy exchangebetween translational, vibrational, rotational and electronic states,storage of potential energy within transient plasma structures orelectric double layers, and ion-acoustic interactions. To reduce thenumber of variables, a shock tube apparatus was used to study theprocesses associated with propagating shocks in a weakly ionized gas ina manner that was largely independent of boundary layer interactions.

In an experimental setup, the shock tube consisted of a high-pressuredriver section and low-pressure section separated by a diaphragm. Gaswas supplied through a bottle system. Air was usually used as the sourcegas but in some tests, carbon monoxide (CO) was also used to seed thegas for spectral signatures. Within the low-pressure section, copperanodes and nickel cathodes, mounted on the upper and lower surfaces,were used to create a uniform electrical discharge that was transverseto the shockwave propagation direction. The maximum available currentwas four amperes provided in constant current mode allowing currentdensities up to ˜150 A/m².

Two laser beams were passed through the driven section and ontophotodetectors to detect the passage of the shockwave after thediaphragm was burst. The photodetectors were thus able to measure bothvelocity and intensity of propagating shocks.

A previously reported main conclusion from the shock tube measurementswas that the shock propagation velocity increased in proportion to thecurrent density, a result that was not inconsistent with purely thermaleffects. (See, Van Wie D. M., Wesner, A. L., and Gauthier, L. R., Jr.,“Shock Wave Characteristics Measured in Gas Discharges,” AIAA Paper99-4824, November 1999.) However, since the gas temperature wasdifficult to measure during the discharge, other possible effects couldnot be ruled out.

To further resolve the effects, new devices and methods were needed tocharacterize the weakly ionized plasma and the unionized gas in theabsence of a propagating shock.

SUMMARY OF THE INVENTION

The damping gyrometer of the invention can be used to measure minuteforces exerted on a rotating body placed within the shock tube medium.In one embodiment, the damping gyrometer comprises at least two and,preferably, four rotating disks or paddles symmetrically mounted to acommon central elevated low-friction pivot point via rising radial arms.The pivot point is the single point of mechanical support for therotating apparatus/means. A stand with a concave glass element/lensprovides a low-friction support as a pivot point seat for the pivotpoint. All elements of the apparatus are non-conductive.

Once set into motion, the only force acting on the gyrometer are thepivot point friction and the damping effects of the medium in which itspins. A laser beam and photodetector (or alternatively a laserdisplacement sensor), along with customized software algorithms are usedto measure the rotational rate and, hence, importantly, the rotationalrate of change overtime or deceleration rate of the apparatus. Thedeceleration of the damping gyrometer can then be used to determineproperties of the medium in which it spins, including changes indensity, pressure, and temperature. The measurement can also be directlyrelated to the electron density in the case of weakly ionized gases.

In the present embodiment, short air blasts through a hollow tube areused to impart momentum to the rotating part of the damping gyrometerand acquired data are post-processed and interpreted offline. In anotherembodiment, the same laser used to determine rotational rate byextracting the paddle location measurements can be used to impartmomentum to the rotating means. A microprocessor can be used to generatethe time/frequency data and to calculate the parameters of the mediumthat are being measured. In this embodiment the rotating apparatus isplaced within a chamber holding the medium of interest and can be set inmotion and non-contact measurements taken through a window into thechamber by purely optical means.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates the damping gyrometer of the invention within aplasma chamber/shock tube and further shows an exploded view of thepivot point seat portion of the invention.

FIG. 2 is a schematic of a shock tube (dimensions in mm).

FIG. 3 illustrates the electrode geometry in the shock tube (dimensionsin mm).

FIG. 4 illustrates a plot of typical frequency versus time spin-down forthe gyrometer of the invention (for current density 26 A/m²).

FIG. 5 illustrates a phase plane plot corresponding to the plot of FIG.4.

FIG. 6 illustrates the relationship between current density and gastemperature in the shock tube based on the measurements with the dampinggyrometer of the invention and theory.

DETAILED DISCLOSURE OF THE INVENTION

The damping gyrometer of the invention is a miniature device that isused to measure minute damping forces exerted on a balanced low-frictionsingle pivot spin mechanism placed within the gaseous medium. As shownin FIG. 1, the gyrometer comprises a vertical fiberglass stand 10 thatsupports a concave glass lens 11, forming the seat 12 for a single pivotpoint rotating mechanism. The rotating mechanism is comprised of asingle insulative inert pivot point 14 that supports four (can be two ormore) symmetrically mounted paddles 16 that extended radially outwardand downward from the center. Both fiberglass and teflon paddles of thesame size and shape can be used. However, the lower density of thefiberglass paddles yield the best data. The stability of the rotatingmechanism is due to the low center of gravity beneath the pivot point.

The gyrometer can be set in motion by a burst of air provided by apluggable hollow dowel 18 (see FIGS. 1 and 3) that penetrates the shocktube 20 (see FIGS. 1-3). At very low pressures the gyrometer can spinfor up to fifteen minutes after an initial revolution rate ofapproximately four rotations per second. As shown in FIG. 1, a laserdisplacement sensor 22 is used to measure the rotational rate of thegyrometer by passing the beam 23 through the Pyrex sidewall of the shocktube and reflecting the beam off the passing addles.

A Matlab routine has been written to convert the measured displacementsensor data into ascribed frequency versus time data for analysis. Ameasurable and repeatable retarding torque was found to act on thegyrometer whenever the plasma state was established. An interpretationof this damping effect based on thermally induced gas viscosity changesyields gas temperature measurements.

A schematic of the shock tube 20 used to perform temperaturemeasurements is shown in FIG. 2. The shock tube is 99 mm in diameter andconsists of a 660 mm long driver section 24, 768 mm driven section 26and a receiver volume 28. The driven section was constructed in twosections made of Pyrex. The upstream section 30 was 508 mm long andcontained a 12×3 cathode array 32. The downstream section 34 is 260 mmlong and contained 7×3 cathode array 36. The downstream section alsocontained a pair of 25.4 mm diameter observation windows 38.

Additional details on the electrode configuration are shown in FIG. 3.The cathode 40 consisted of an array of conical Ni-200 electrodes 42.The axial spacing of the electrodes is 30 mm and the angular spacing is35°. The conical tip is 120° total included angle, and is 12.7 mm indiameter with the tip 3.7 mm above the surface of the Pyrex tube. Theanode 44 consists of two copper plates located along the upper surfaceof the driven section. The anode in the upstream driven section is 355.6mm long with an arc-length of 67 mm. The anode in the downstream drivensection is 184 mm long with an arc-length of 67 mm. The anode andcathode electrodes begin 107 mm downstream from the diaphragm.

The discharge was generated using one or two Universal Voltronics ModelBRC-5-2000R-STD-3PH-200V DC power supplies in parallel. Each powersupply was operated in a constant current mode with the capability ofproducing up to 5000 V and 2 A.

Prior to investigating shock propagation characteristics in the plasma,a characterization of the undisturbed plasma was undertaken.Measurements were taken of the rise and fall time of the dischargecurrent waveforms both on the cathodic and the anodic side of the testchamber. Measurements indicate the power supply established a steadydischarge within 20 milliseconds after turn-on. The waveforms showed acharacteristic current spike of 1 millisecond duration and 2-5 times thesteady state value during the plasma turn-on time. Extinction of thedischarge current occurred in approximately 1 millisecond. The plasmawas homogenous in appearance.

The shock tube has two transverse diagnostic ports 38, 39 which are usedto direct the infrared energy beam through KBr windows. A globar notshown is used to provide the infrared beam. In tests where a CO seed wasused, a small needle valve was used to allow the CO gas into the shocktube prior to a test.

To test the damping gyrometer, it was placed into the shock tube nearthe upstream electrodes. A large rubber diaphragm 46 in FIGS. 2 and 3was used to seal the tube. A hollow fiberglass tube 18 passed throughthe rubber diaphragm was used to provide the short burst of air neededto set the gyrometer in motion. A laser displacement sensor (LAS 8010V)22 was used to measure the distance to each paddle of the gyrometer asit passed by aiming the laser through the Pyrex sidewall 48 in FIG. 1 ofthe shock tube. Several oscilloscopes were used to acquire data from thelaser displacement sensor. It was necessary to sample the laserdisplacement sensor at least once every millisecond to be able toresolve the paddle position.

A Matlab routine processed the output from the laser displacement sensorand produced a time/frequency series corresponding to the state of thegyrometer as it spun down. The need for 1 millisecond sampling rate andlong spin down times (up to several minutes) created large data filesduring measurements that covered a significant portion of a spin (256seconds). For each paddle, adjacent times of passage T_(i) and T_(j)were used to compute an ascribed time and ascribed frequency. Theascribed time is (T_(i)+T_(j))/2 and the ascribed frequency is1/(T_(j)−T_(i)). The time/frequency series were then converted intophase plane plots that showed the relationship between the frequency andits derivative.

The greatest difficulty encountered during the gyrometer tests waseliminating external influences. The most problematic was air leakagearound the electrodes and other rig openings as the plasma heated up.The mass of the fiberglass paddles of the damping gyrometer was only7.95 grams. Fortunately, when the data was processed, the leakageeffects were revealed by anomalies such as the gyrometer increasing itsfrequency for short periods of time. Data sets with clear leakageeffects were not used.

It should also be pointed out that the damping gyrometer used in theseexperiments was much more massive than radiometer type devicesinvestigated by others that depend on the thermal effects caused byincident radiation to impart motion In any event, the heating of thedamping gyrometer itself was symmetrical by construction and thusheating effects on the gyrometer itself should not impart net motion.The laser used by the laser displacement sensor was small enough (1 mW)to preclude heating or the imparting of momentum.

The damping gyrometer within the shock tube is shown in FIG. 1. Thegyrometer exploits properties of fluids in the creeping flow regime,best described by exceedingly low Reynolds number. Computing theReynolds numbers for the flow about the gyrometer paddles based on thegeometry of the gyrometer produces the following range for revolutionrates (f) from 1-3.5 revolutions per second and pressures from 1 to 10Torr.${Re} = {\frac{\rho \quad {UD}}{\mu} = \frac{2\pi \quad {rfPD}}{\Re \quad T\quad \mu}}$

where,

f is the rate of revolution=1-3.5 Hz

r is the moment arm=1 in (0.0254 m)

P is the pressure range=0.0193-0.193 psi

D is the paddle diameter=1 in (0.0254 m)

R is the gas constant for air=1716 ft-lb/(slug R)

T is gas temperature=530 R (294 K)

μ is the viscosity=2.11E-5 lb-s/ft²

U is the paddle velocity=2πrf

This yields Reynolds Number of:

0.006<Re<0.3

This range of Reynolds numbers is within the flow regime known ascreeping motion or flow. Stokes' solution for an immersed sphereemploying creeping motion led to several extraordinary properties ofthis type of flow:

1) The streamlines and velocities are entirely independent of the fluidviscosity.

2) The streamlines possess perfect fore-and-aft symmetry.

3) The local velocity is everywhere retarded from its freestream value.

4) The freestream disturbance extends to enormous distances.

The most extraordinary result found was for the total drag forcedeveloped by integrating the pressure and shear around the surface.

F=6πμUD

Note that the drag force on the sphere (and any similar body withincreeping flow) is independent of tie fluid density.

In principle, a Stokes flow analysis is possible for anythree-dimensional body shape. Contained within these solutions is theexact result for a disk normal to the freestream.

F=16μUD

Again note that this result is independent of the freestream gasdensity.

Thus, the drag on the gyrometer paddles should be directly proportionalto the viscosity, the paddle diameters, and the paddle rotational rates.

F _(paddles) ∝μU _(paddles) D

This translates into a retarding torque on the gyrometer given by thefollowing equation.

T _(Aerodynamic) ∝rμUD

The total torque on the body is composed of the aerodynamic drag,following the functional form given above, and the torque from the pivotdrag.

T _(Total) =T _(Aerodynamic) +T _(Friction)

The torque from the friction is proportional to the pivot radius and thematerial coefficient of friction. It is only necessary that it is smalland not sensitive to temperature variations.

T _(Friction) ∝r _(Pivot)μ_(k)

Kinematics dictates that the angular deceleration, α, is given by thefollowing formula: $\alpha = \frac{T_{Total}}{I}$

where, I is the damping gyrometer moment of inertia.

Thus,

α∝μ(T)U+const

Assuming the temperature is constant, then,

α∝U+const

Given that U, the paddle velocity, for the gyrometer is a constant timesthe rotational rate, the following relational function for thederivative of the gyrometer rotational frequency is seen.

−f′=af+const

Finally, since the proportionality constant, a, is directly related tothe temperature through the gas viscosity, the slope of the linerelating f and −f′ for a single spin (needed to insure a uniformfriction) is an indirect measure of the gas temperature. FIG. 4 shows atypical frequency versus time spin down plot for the gyrometer (forcurrent density 26 A/m²). FIG. 5 shows the corresponding phase planeplot.

The proportionality constant, a, between the gyrometer frequency f andits negative derivative (−f′) was found to increase with increasingcurrent density in the shock tube. Theory ties this to the gastemperature. FIG. 6 shows the relationship between current density andgas temperature in the shock tube based on the measurements with thedamping gyrometer and the theory. The temperature corresponding to themeasured gyrometer characteristics at the 40 A/m² current density asused during the measurements made using a fast scanning FourierTransform Infrared Spectrometer (FTIR) yields 1435 K.

Possible electrical effects were not addressed during the discussionabove. Only insulative materials were used in the construction of thegyrometer. The paddles were made of fiberglass and the pivots that wereused were made of either boron nitride or fiberglass. A glass tip wasused with the fiberglass pivot since early testing showed that the pivotpoint friction increased greatly under heating when the fiberglass wasused as the tip.

Electrostatic influences were found to be negligible based on comparisonof spin downs at atmospheric pressure with and without 5 KV appliedacross the electrodes. No current flow occurred during these tests dueto the higher insulative properties of the air at the higher pressure.Based on comparison of the spin down plots, any induced electrostaticcharges were balanced and did not significantly affect the motion of thedevice. While reactive effects due to the paddles disturbing the currentflow cannot be completely ruled out, the agreement of the thermalinterpretation of the device with the spectroscopic measurementsindicates that the temperature is the dominant variable that controlsthe gyrometer response.

The calculation of the expected gas temperature based on the measuredshock velocity within the gas was accomplished using the standardone-dimensional unsteady shock tube equations. This is a simplifiedanalysis and does not include any effects from non-uniform temperaturedistributions known to be present within the ionized gas, the timerequired to initially develop or accelerate the shock, etc. Also, acomplication is introduced since the shock initially forms within a coldgas and then travels into a region of higher temperature (the region ofgaseous ionization).

Using measured values of the shock propagation velocity in cold flow(800 m/s) and knowing the cold gas temperature (300 K) and pressure (1Torr), the strength of the shock and all aerodynamic properties behindthe shock are calculated for the initial development of the shock withinthe cold region. When the shock enters the region of elevatedtemperature, the shock accelerates and an expansion wave is reflectedfrom the boundary.

A second shock calculation, similar to the initial calculation, isperformed. This calculation is performed iteratively, as the driver gashas a velocity, induced by the passage of the non-accelerated shock.Knowing the measured shock velocity within the plasma (970 m/s) at acurrent density of 40 A/m², a plasma temperature was assumed, and thepressure values on both sides of the contact surface were calculated. Ifthe pressures on either side of the contact surface did not match, theassumed plasma temperature was adjusted until the pressure differenceacross the contact surface reached zero. To produce a shock velocity of970 m/s within the plasma, a temperature of 1135 K was calculated withthis method. Table III is a comparison of the gas temperature resultsfrom various approaches at a current density of 40 A/m².

TABLE III Summary of Gas Temperature Results for 40 A/m² Current DensityMethod Pressure (Torr) Temperature (K.) FTIR P & R branches 3 1335 FTIRP Branch 3 1453 Damping Gyrometer 1-10 1435 Lossless 1D Analysis 1 1135Thermocouple 1-10 560

A temperature of 1400 K was found to produce a shock velocity of ˜1060m/s. This is less than 10 percent error over the measured shock velocityin the ionized gas. A temperature of 1500 K yields a shock velocity of1090 ms, which is less than 13 percent lower. Thus, the dampinggyrometer of the invention yielded a very similar temperaturemeasurement for the same current as did FTIR which temperaturemeasurement was also consistent with a lossless one-dimensionalcomputation based on the measured shock velocity changes that wereobserved previously.

What is claimed is:
 1. A damping gyrometer for determining a property ofa gaseous medium comprising: a vertical stand comprised of an insulatingand chemicaly inert material; a rotating means, comprised of aninsulating and chemically inert material, mounted on the stand, therotating means comprising: a pivot point; and at least two paddles, thepaddles being symmetrically mounted to the pivot point and extendingradially outward and downward therefrom; means for setting the rotatingmeans in motion; means for measuring the rate of rotation of therotating means to determine the deceleration of the rotating means; andmeans for determining the property of the gaseous medium using thedeceleration of the rotating means.
 2. The gyrometer as recited in claim1, further comprising a pivot point seat supported by the stand, thepivot point of the rotating means being mounted on the pivot point seat.3. The gyrometer as recited in claim 2, the pivot point seat comprisinga concave glass lens.
 4. The gyrometer as recited in claim 1, whereinthe paddles are fiberglass.
 5. The gyrometer as recited in claim 1,wherein the tip of the pivot point is glass.
 6. The gyrometer as recitedin claim 1, the setting in motion means comprising a hollow tube forsupplying a burst of air.
 7. The gyrometer as recited in claim 1, thesetting in motion means comprising a laser for supplying a laser beam.8. The gyrometer as recited in claim 1, the means for measuring the rateof rotation comprising a laser.
 9. A method for determining a propertyof a gaseous medium comprising the steps of: placing a rotating means,comprised of an insulating and chemically inert material, in the gaseousmedium; setting the rotating means in motion; measuring the rate ofrotation of the rotating means to determine the deceleration thereof;and determining the property of the gaseous medium using thedeceleration.